Domanda del libro di testo
FIGURE EX10.28 shows the potential-energy diagram for a 500 g particle as it moves along the x-axis. Suppose the particle's mechanical energy is 12 J. Where are the particle's turning points?
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Ch 10: Interactions and Potential Energy
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 10, Problema 29
In FIGURE EX10.28, what is the maximum speed a 200 g particle could have at x = 2.0 m and never reach x = 6.0 m?
Guida verificata passo dopo passo1
Step 1: Analyze the graph provided. The graph shows the potential energy U(x) as a function of position x. At x = 2.0 m, U(x) = 0 J, and at x = 6.0 m, U(x) = 4 J. The particle's total mechanical energy must be less than or equal to 4 J to ensure it does not reach x = 6.0 m.
Step 2: Use the principle of conservation of mechanical energy. The total mechanical energy E is the sum of the kinetic energy K and potential energy U. At x = 2.0 m, the potential energy U is 0 J, so the total energy E is equal to the kinetic energy K at this position.
Step 3: Write the expression for kinetic energy K: \( K = \frac{1}{2} m v^2 \), where m is the mass of the particle and v is its speed. The mass of the particle is given as 200 g, which should be converted to kilograms: \( m = 0.2 \, \text{kg} \).
Step 4: Set the total energy E equal to the maximum allowable energy (4 J) to ensure the particle does not reach x = 6.0 m. Solve for the maximum speed v using \( E = \frac{1}{2} m v^2 \). Rearrange the equation to find \( v = \sqrt{\frac{2E}{m}} \).
Step 5: Substitute the values for E (4 J) and m (0.2 kg) into the equation \( v = \sqrt{\frac{2E}{m}} \). This will give the maximum speed the particle can have at x = 2.0 m without reaching x = 6.0 m.
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Potential Energy (U)
Potential energy is the energy stored in an object due to its position in a force field, such as gravitational or elastic fields. In the context of the graph, it represents the energy of the particle at various positions along the x-axis. The height of the curve indicates the potential energy at each position, which influences the particle's ability to move to different locations.
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06:35
Gravitational Potential Energy
Conservation of Energy
The principle of conservation of energy states that the total energy in a closed system remains constant. For the particle in the problem, the sum of its kinetic energy and potential energy must equal a constant value. This means that as the particle moves, any change in potential energy will result in a corresponding change in kinetic energy, affecting its speed at different positions.
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06:24Conservation Of Mechanical Energy
Kinetic Energy (KE)
Kinetic energy is the energy of an object due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In this problem, the maximum speed of the particle at x = 2.0 m can be determined by considering the potential energy at that point and ensuring that the particle has enough kinetic energy to not reach x = 6.0 m, where the potential energy is higher.
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06:07Intro to Rotational Kinetic Energy
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